Taylor, who follows Gareth Barry from Villa Park to City, will serve as back-up to first-choice goalkeeper Shay Given, with Hart expected to join Birmingham in a season-long switch in the coming days.
The 28-year-old Taylor spent four years at Villa after joining from Arsenal.
Taylor revealed he chose City after speaking to Villa's number one Brad Friedel, who knows boss Mark Hughes from their days together at Blackburn.
"I talked to Brad for some advice and he couldn't speak highly enough of the manager and his goalkeeping coach Kevin Hitchcock," Taylor told City's official website.
"He has a high regard for Kevin as a person as well as a coach and I can't wait to start. This is a fantastic club to be joining, a club that is going places with a great new owner and a manager I have a lot of respect for."
Taylor, who collected a Premier League winner's medal with Arsenal in 2002, spent part of last season on loan at Cardiff after falling down the Villa pecking order behind Friedel and Brad Guzan.
However, Hughes believes he is the right man to keep pressure on Given.
"We are delighted to be able to add a goalkeeper of Stuart's undoubted calibre to the squad," Hughes said.
"Stuart is still a fairly young goalkeeper at 28 but he provides a wealth of experience and reliability."
Taylor's arrival gives City the cover they need to allow Hart to go out on loan.
The England Under-21 keeper has made no secret of his desire for first-team football since being squeezed out of the City team by the arrival of Given in January.
Capped once by England at senior level, the 22-year-old Hart has his eye on a place in Fabio Capello's World cup squad next summer, and is expected to seal a loan move to Birmingham in the coming days.